Estimation of daily reference evapotranspiration without the need for wind speed using machine learning and hybrid models in Tabriz and Urmia synoptic stations

Abstract
Background and Objectives: Evapotranspiration is considered as the water requirement for plants. Therefore, its measurement is necessary for all agricultural and irrigation projects. Evapotranspiration is one of the main components of the hydrological cycle associated with agricultural systems. Usually, evapotranspiration can be obtained using reference evapotranspiration (ET0). Accurate estimation and prediction of ET0 is essential in managing water resources, planning irrigation, and determining the water requirement of plants. Prediction of the ET0 by providing information about the future state in different time scales can help to make appropriate decisions, plan, and apply water resources management methods. Also, assessing agricultural drought conditions by well-known indices such as the Standardized Precipitation-Evaporation Index (SPEI) and Palmer Drought Severity Index (PDSI) directly requires ET0 of the region. The sharp decrease in the level of Lake Urmia and the threat to the region's ecosystem have also made the need for accurate calculation of ET0 more significant than in the past. One of the solutions to calculate ET0 is to use the FAO-56 Penman-Mantis equation (FAO-56 PM), an acceptable alternative for the scarce lysimeter data. However, the Penman-Mantis equation is highly dependent on the wind speed parameter, so a small error in the wind speed measurement causes a significant error. Therefore, this study aims to provide an innovative and reliable model for estimating ET0 without the need for wind speed parameters in Tabriz and Urmia stations.
Methodology: In this study, to predict daily ET0 different intelligent models including multi-layer perceptron neural network (ANN-MLP), support vector regression (SVR), and support vector regression combined with firefly algorithm (SVR-FFA) were used in Urmia and Tabriz stations during 2002-2022 period. The input parameters of the models included minimum relative humidity (RHmin), maximum relative humidity (RHmax), average relative humidity (RHavg), sunshine hours (SSH), minimum temperature (Tmin), maximum temperature (Tmax), average temperature (Tavg), and average soil temperature (Tsoil) which were obtained from Iran Meteorological Organization (IRIMO). Also, four different scenarios were used to run the models. The selection of different input combinations was based on the correlation coefficient, so the first combination had the lowest correlation and the last combination had the highest correlation concerning ET0. Also, data from 2002-2015 for 14 years were considered for model training and from 2016-2022 for 6 years for model testing. Correlation coefficient (R), mean absolute error (MAE), root mean square error (RMSE), and normalized root mean square error (NRMSE) indices were used to evaluate the used models.
Findings: The comparison and evaluation of the models used in Tabriz station showed that the SVR-FFA-4 model was chosen as the best model in this station with the root mean square error of 1.23 mm day-1. Among the SVR models, the SVR-4 model showed a good performance with the root mean square error of 1.95 mm day-1 after the combined model. Finally, the ANN-4 model also obtained an acceptable accuracy compared to other ANN combinations by having the root mean square error of 1.99 mm day-1. Finally, the evaluation of the results used for the Urmia station shows that the SVR-FFA-3 model has made the best predictions compared to other models with a root mean square error of 1.16mm day-1. The SVR-3 and SVR-4 models had a higher accuracy than other SVR combinations with a root mean square error of 1.78 mm day-1, but the third scenario was chosen as the appropriate model in the SVR model due to having less input. Among the ANN combinations, the ANN-3 model has a good performance compared to the other combinations of this model with the root mean square error of 1.81 mm day-1.
Conclusion: The results of this study showed that in both studied stations, the hybrid model showed higher accuracy than the individual models. So, in Tabriz station, the SVR-FFA-4 model had the best performance with an error rate of 1.23 mm day-1. In the Urmia station, the SVR-FFA-3 model showed good accuracy with an error rate of 1.16 mm day-1. Finally, it is suggested to use the hybrid model to predict the daily reference evapotranspiration in the northwest of the country. One of the limitations of this research is the lack of access to the parameters of dew point temperature and solar radiation. Therefore, it is suggested to use these parameters in the subsequent studies.